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If the three points (a,b),(a+kcosalpha,b...

If the three points (a,b),`(a+kcosalpha,b+ksinalpha)and(a+kcosbeta,b+ksinbeta)` are the vertices of an equilateral triangle , then which of the following is true and why ?
(i) `|alpha-beta|=(pi)/(4)` , (ii) `|alpha-beta|=(pi)/(2)`
(iii) `|alpha-beta|=(pi)/(6)` , (iv) `|alpha-beta|=(pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
`cos(alpha-beta)=(1)/(2)="cos"(pi)/(3)therefore|alpha-beta|=(pi)/(3)`.
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